1. Field of the Invention
This invention relates to digital signal processing; and, in particular, this invention relates to equalization and demodulation of signals which are modulated with a repetitive component.
2. Discussion of the Related Art
In many applications involving digital signals (i.e. signals which are sampled at discrete times), the transmitted signals are digitally modulated. Often, digital modulation results in a signal ("structured signal") which is not completely random but has some repetitive structure. For example, under a time-division multiplexing (TDM) protocol, multiple data streams ("tributary data streams") are interleaved to form a signal having a repetitive structure. Such a signal is typically divided into frames consisting of a number of time slots each assigned to a tributary data stream for transmission of its data. Usually, one or more markers ("fixed bits") are placed at predetermined time slots of a frame for synchronization. Often, multiple frames in turn form a "superframe", which is an even larger repetitive unit of the transmitted signal. Synchronization between the recipient and the signal transmitter is further enhanced by additional markers placed at predetermined time slots to demarcate the superframe. In addition, in a typical TDM signal, training sequences are periodically inserted at for synchronization of baud and carrier signals at the receiver, and for equalization adaptation. Hence, a number of inserted bit sequences form repetitive components in the TDM signal. In addition, if a tributary data stream is self-correlated, the resulting time-multiplexed signal will be periodically correlated.
A channel or transmission medium can impose distortion upon a signal transmitted through it. For example, in a crowded communications environment, signals can interfere with each other. In a mobile communications system, a signal may arrive at a receiving point via multiple paths at different times, leading to multipath distortions. These and other distortions can cause errors in demodulating the signal, leading to errors in recovering the transmitted symbols at the receiver. To mitigate the distortions in the channel, an adaptive equalizing filter ("adaptive equalizer") is often applied to the received signal. In such an adaptive equalizer, the weights of the filter adapt to the changing characteristics of the channel..sup.1 One class of adaptive equalizers is collectively known as adaptive linear equalizers.sup.2. FNT .sup.1 In a digital filter, the number of weights in a filter corresponds to the number of signal samples used to generate the output sample. FNT .sup.2 An adaptive equalizer is an adaptive linear equalizer when the output value of the adaptive equalizer is a linear combination of its input value or values.
FIG. 1 is a block diagram representing the signal equalization and demodulation system 100 in a receiver. As shown in FIG. 1, a received signal is demodulated by element 101 to a base band signal by removing the carrier frequency f.sub.c. The base band signal is then sampled by sampling device 102, at either the symbol interval, or a fraction of the symbol interval. In many systems, a tracking device 103 is provided to maintain sampling at a proper phase of the base band signal, The samples of the base band signal are then provided to an adaptive linear equalizer 110, represented in FIG. 1 by filter 105, error means 108 and filter weight update means 107. (When the base band signal is sampled at the symbol interval, the equalizer is known as a "T-spaced equalizer". Otherwise, i.e. when the base band signal is sampled at a fraction of the symbol interval, the equalizer is known as a "fractionally spaced equalizer".)
Generally, in an adaptive linear equalizer, such as adaptive linear equalizer 110, a finite transversal filter 105 computes a weighted sum of a number samples of the base band signal. This weighted sum is then provided to a decision device 106 to determine the symbol received (the "symbol decision"). In one type of equalizer, which is shown in FIG. 1, the decision device 106 provides a feedback signal to adaptively modify the weights of finite transversal filter 105. Such an equalizer is known as a "decision-directed", or "blind", equalizer.
As shown in FIG. 1, a phase-corrected output value 121 of transversal filter 105 and the symbol decision 122 of decision device 106 are fed back to error means 108 to generate an error signal 120. In FIG. 1, phase correction in the output value 121 of transversal filter 105 is provided by circuit 109, which compares the phases of the symbol decision 122 and the output value 123 of transversal filter 105 to detect any residual carrier-tracking phase error. The error signal 120 generated by error means 108 represents, assuming that the data symbol is correctly recovered, both amplitude and phase errors in the phase-corrected output value 121 of finite transversal filter 105. When a training sequence of data symbols is available, error signal 120 is generated by computing, at each time point, a complex difference between the phase-corrected sample 121 of the equalizing digital filter and the expected corresponding data symbol in the training sequence. Error signal 120 is fed into filter weight update means 107 to modify the weights of finite transversal filter 105. In FIG. 1, the phase error detected by phase correction device 109 is reintroduced into error signal 120, which is then provided to filter weight update means 107.
The feedback signal received by filter weight update means 107 can also be obtained by biasing ("respinning") symbol decision device 106 by the phase error and computing the complex difference between the respun symbol decision and the output value 123 of transversal filter 105.
Several algorithms exist to generate adaptively the weights of an adaptive linear equalizer. One common method is the least-mean-square (LMS) algorithm, first described by R. W. Lucky et al ("Lucky's LMS algorithm"). An overview of Lucky's LMS algorithm can be found in "Adaptive Equalization," by Shahid Qureshi, published in IEEE Communications Magazine, March, 1982, pp. 9-16. Improvements based on Lucky's LMS algorithm include (i) the recursive least squares (RLS) methods, such as those described in "Application of Fast Kalman Estimation to Adaptive Equalization," by D. D. Falconer and L. Ljung in IEEE Transactions of Communications, Vol. Com-26, No. 10, October 1978, pp. 1439-45; and (ii) the adaptive lattice methods, such as those described in "Lattice Filters for Adaptive Processing," by B. Friedlander in Proceedings of the IEEE, Vol. 70, No. 8, August 1982, pp. 829-67. These improvements are designed to converge more rapidly than Lucky's LMS algorithm. Other improvements upon Lucky's LMS method include methods which adjust the weights of the equalizing digital filter to optimize a characteristic of the desired signal. One example of such methods is the dispersion-directed method described in "Self-recovering Equalization and Carrier Tracking in Two-dimensional Data Communication Systems," by D. Godard, IEEE Transactions on Communications, Vol. Com-28, No. 11, November 1980, pp. 1867-75.
Another architecture for adaptive linear equalization is the decision feedback equalizer (DFE). The DFE equalizer architecture consists of both a forward digital filter, which computes a weighted sum of input samples, similar to those based on Lucky's LMS described above, and a feedback digital filter which computes a weighted sum of data symbols determined in previous symbol decisions. In a DFE equalizer, the numbers of coefficients in the forward and feedback filters can be different. The decision process is applied to the sum of the output values of the forward and backward equalization filters to generate a symbol. As in all adaptive equalizers, an error signal is provided to update the filter weights and to improve filter performance.
Yet another adaptive equalization method, which uses an artificial neural network (ANN), is described by S. Siu, G. J. Gibson and C. F. N. Cowan in "Decision Feedback Equalizer Using Neural Network Structures," IEE Proceedings, 137(4): 221-5, 1990. In the ANN method, the signal samples are sequentially provided as input; samples into each ANN processing unit of a first layer of a neural network. The output samples of the first layer's processing units are then provided as input samples into each processing unit of a second layer of the ANN. The output samples of the processing units in this second layer are then provided as input samples into a single output processing unit. A decision process is then applied to each output sample of the output processing unit to generate a symbol. In this ANN, each processing unit consists of a finite transversal filter with adjustable weights, and a nonlinear functional operator which operates on the output sample of the finite transversal filter. The filter weights of the transversal filter are computed during the processing of a training sequence. The error signal for the ANN is obtained by subtracting from each data symbol of a training sequence from the corresponding data symbol output of the output processing unit. A back propagation algorithm is used to generate new coefficients for each processing unit. The ANN architecture can also incorporate feedback using previously decided symbols to become a decision feedback ANN architecture.
Each of the methods discussed above in the prior art processes sequential signal samples to generate, for each iteration, one output symbol and an error signal. The error signal is used in an updating procedure for filter weights to adaptively modify the transversal filters of the equalizer for the next iteration. The equalizer, with the updated filter weights, is then used to generate the next symbol. The process continues until all symbols are decoded one by one.
The methods used in the prior art assume that the symbols in the input data are random. However, when the input signal is a structured signal, i.e. the signal includes a periodic component, the filter adaptation process generates transversal filter weights that are skewed by the periodic component. Consequently, the periodic component of the input signal is amplified while the aperiodic component of the input signal is attenuated. Recalling that, in a structured signal such as a TDM signal, the periodic component is substantially an artifact of the signal protocol, e.g. the framing structure, and often does not relate to the tributary data being transmitted, the amplification of the periodic component is therefore undesirable. Thus, to enhance the performance of a prior art method operating on a signal with a periodic component, one approach requires the signal to be randomized prior to transmission and derandomized at the receiver after equalization. The additional costs of the randomization and derandomization steps add to system cost, complexity, and processing time.
Another approach taken in the prior art to overcome the overweighting of the periodic components of a signal uses an equalizing filter comprising a tapped delay line which takes into account only signal samples spanning a time period shorter than the period of the framing information. However, this approach reduces the frequency resolution of the equalizer and handicaps the equalizing filter's ability to excise signal interference and multipath effects.
Yet another prior art approach prevents further updates to filter weights after the filter has converged to some useful value, but prior to the time the filter weights begin to destroy the aperiodic or "random" data. However, this approach also reduces the equalizer's capability to reject interference and to compensate for distortion.